Conformal thin-sandwich solver for generic initial data

2012/08/31 by William E. East, Fethi M. Ramazanoğlu, Frans Pretorius
Mathematics · Physics and Astronomy · #Applied mathematics #Astrophysical Phenomena and Observations #Classical mechanics #Collision #Computer science #Conformal map #Einstein #Einstein field equations #Flatness (cosmology) #Gamma-ray bursts and supernovae #Gravitational singularity #Mathematical analysis #Mathematical optimization #Mathematics #Multigrid method #Partial differential equation #Physics #Pulsars and Gravitational Waves Research #Quantum mechanics #Solver #Superposition principle #gr-qc

paper · pdf · doi:10.1103/physrevd.86.104053

published as Phys. Rev. D 86, 104053 (2012) · 12 pages, 8 figures, PRD in production

arxiv created 2012/11/06 · openalex publication_date 2012/11/27 · arxiv updated 2012/11/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We present a new scheme for constructing initial data for the Einstein field equations using the conformal thin-sandwich formulation that does not assume conformal flatness or approximate Killing vectors. This includes a method for determining free data based on superposition, as well as a way to handle black hole singularities without excision. We numerically solve the constraint equations using a multigrid algorithm with mesh refinement. We demonstrate the efficacy of the method with initial data solutions for several applications: a quasicircular binary black hole merger, a dynamical capture black hole-neutron star merger, and an ultrarelativistic collision.

Citations

• Weakly Turbulent Instability of Anti–de Sitter Spacetime
• Initial data and coordinates for multiple black hole systems
• Binary Neutron Stars in General Relativity: Quasi-Equilibrium Models
• Simulation of asymptoticallyAdS5spacetimes with a generalized harmonic evolution scheme
• Construction of initial data for 3+1 numerical relativity
• Alternatives to standard puncture initial data for binary black hole evolution
• Binary black hole initial data for numerical general relativity based on post-Newtonian data
• Approximate analytical solutions to the initial data problem of black hole binary systems
• Corotating and irrotational binary black holes in quasicircular orbits
• Head-on collisions of unequal mass black holes inD=5dimensions
• Large Mass Hierarchy from a Small Extra Dimension
• Is super-Planckian physics visible? Scattering of black holes in 5 dimensions
• Initial data for black hole–neutron star binaries: A flexible, high-accuracy spectral method
• Measuring eccentricity in binary black-hole initial data
• Comparing initial-data sets for binary black holes
• Relativistic numerical model for close neutron-star binaries
• Quasiequilibrium binary black hole sequences for puncture data derived from helical Killing vector conditions
• The Hierarchy Problem and New Dimensions at a Millimeter
• Black holes from high-energy beam--beam collisions
• Conformal “Thin-Sandwich” Data for the Initial-Value Problem of General Relativity
• Detector configuration of KAGRA - the Japanese cryogenic gravitational-wave detector
• High-velocity collision of two black holes
• Numerical Approaches to Spacetime Singularities
• Binary Neutron Star Mergers
• Wormholes and trumpets: Schwarzschild spacetime for the moving-puncture generation
• Ultrarelativistic Particle Collisions
• Theorems on Existence and Global Dynamics for the Einstein Equations